Answer:
[tex] \boxed{ \boxed{ \bold{ \purple{ \sf{28.53 \: {units}^{2} }}}}}[/tex]
Option C is the correct option.
Step-by-step explanation:
For ABD
[tex] \sf{ = \frac{2.89 + 8.59 + 8.6}{2} }[/tex]
[tex] \sf{ = \frac{20.08}{2} }[/tex]
[tex] \sf{ = 10.04}[/tex]
∆ ABD = [tex] \sf{ = \sqrt{10.04(10.04 - 2.89)(10.04 - 8.59)(10.04 - 8.6)} }[/tex]
[tex] \sf{ = \sqrt{10.04 \times 7.15 \times 1.45 \times 1.44 }}[/tex]
[tex] \sf{ = \sqrt{149.8891} }[/tex]
[tex] \sf{ = 12.2429}[/tex]
For ∆ ACD ,
[tex] \sf{s = \frac{8.6 + 4.3 + 7.58}{2} }[/tex]
[tex] \sf{ = \frac{20.48}{2} }[/tex]
[tex] \sf{ = 10.24}[/tex]
∆ ACD = [tex] \sf{ = \sqrt{10.24(10.24 - 8.6)(10.24 - 4.3)(10.24 - 7.58} }[/tex]
[tex] \sf{ \sqrt{10.24 \times 1.64 \times 5.94 \times 2.66} }[/tex]
[tex] \sf{ = \sqrt{265.3456} }[/tex]
[tex] \sf{ = 16.2894}[/tex]
Area of quadrilateral ABCD = [tex] \sf{12.2429 + 16.2894}[/tex]
[tex] \sf{ = 28.5323}[/tex]
[tex] \sf{ = 28.53}[/tex] units ²
Hope I helped!
Best regards!
